Sökning: "Subalgebra"

Visar resultat 1 - 5 av 8 uppsatser innehållade ordet Subalgebra.

  1. 1. Classification of almost monomial subalgebras of small codimension

    Kandidat-uppsats, Lunds universitet/Matematik LTH; Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/Matematikcentrum

    Författare :Ludvig Sundell; [2023]
    Nyckelord :Algebra; Subalgebra; Polynomial; SAGBI basis; LAGBI basis; Lower semigroup; Mathematics and Statistics;

    Sammanfattning : In this text, we study almost monomial subalgebras using LAGBI bases. We introduce the concept of a LAGBI base and present an algorithm for computing them. We then use this algorithm to find, and present in a table, all polynomial subalgebras with Frobenius number smaller than or equal to ten. LÄS MER

  3. 2. On Geometric Number

    Kandidat-uppsats, Uppsala universitet/Analys och partiella differentialekvationer

    Författare :Petter Gunnarsson; [2023]
    Nyckelord :clifford algebra; hypercomplex number; octonion;

    Sammanfattning : This is an overview of geometric algebras in dimensions 0-4 from the perspective of the concept of number itself. It is developed from a historic viewpoint and investigates and develops a pedagogic approach emphasizing the geometric aspects of the subject. LÄS MER

  4. 3. Constructing Subalgebras of K[x] Using the Minimal Polynomial

    Master-uppsats, Lunds universitet/Matematik LTH

    Författare :Marianne Ljunggren; [2023]
    Nyckelord :Algebra; Subalgebra; Polynomial Algebra; Minimal Polynomial; Mathematics and Statistics;

    Sammanfattning : In this report we will be working with subalgebras A of finite codimension in K[x]. It is known that such subalgebras can be expressed using a set of linear conditions evaluated at a finite set of points called the spectrum elements of A. LÄS MER

  5. 4. The Ext-Algebra of Standard Modules of Bound Twisted Double Incidence Algebras

    Master-uppsats, Uppsala universitet/Algebra, logik och representationsteori

    Författare :Mika Norlén Jäderberg; [2023]
    Nyckelord :Algebras; Finite-dimensional; Partially ordered sets; Modules; Quasi-hereditary; Ext-algebra; Schur algebra; Quiver; Path algebra; Categories; Morita equivalence; Yoneda product; Standard module; Homological algebra; Cohomology; Anick Chains;

    Sammanfattning : Quasi-hereditary algebras are an important class of algebras with many appli-cations in representation theory, most notably the representation theory of semi-simple complex Lie-algebras. Such algebras sometimes admit an exact Borel sub-algebra, that is a subalgebra satisfying similar formal properties to the Borel sub-algebras from Lie theory. LÄS MER

  7. 5. Zero Spectrum Subalgebras of K[x] Described by Higher Derivatives

    Kandidat-uppsats, Lunds universitet/Matematik LTH

    Författare :Erik Kennerland; [2023]
    Nyckelord :Algebra; Almost Monomial Subalgebra; Derivation; Lower Degree; Lower Semigroup; Subalgebra Spectrum; Truncation; Mathematics and Statistics;

    Sammanfattning : Unital subalgebras of finite codimension in the polynomial ring $\mathbb{K}[x]$ are described by a finite number of so called subalgebra conditions over a finite set in $\mathbb{K}$ named the subalgebra spectrum. Restricting attention to subalgebras whose spectrum is the singleton $\{0\}$ reveals a rather well behaved class of subalgebras, called almost monomial from the fact that these contain an ideal consisting of all monomials above a certain degree. LÄS MER